\(\begin{aligned} {\text{Prevalence}} = \frac{\text{TP + FN}}{\text{TP + FP + TN + FN}} \end{aligned}\)
\(\begin{aligned} \text{Sensitivity (Recall, True Positive Rate)} = \frac{\text{TP}}{\text{TP + FN}} = \frac{\text{TP}}{\text{Real Positives}} = \text{Prob( Predicted Positive | Real Positive )} \end{aligned}\)
\(\begin{aligned} \text{Specificity (True Negative Rate)} = \frac{\text{TN}}{\text{TN + FP}} = \frac{\text{TN}}{\text{Real Negatives}} = \text{Prob( Predicted Negative | Real Negative )} \end{aligned}\)
\(\begin{aligned} \text{PPV (Precision)} = \frac{\text{TP}}{\text{TP + FP}} = \frac{\text{TP}}{\text{Predicted Positives}} = \text{Prob( Real Positive | Predicted Positive )} \end{aligned}\)
\(\begin{aligned} \text{NPV} = \frac{\text{TN}}{\text{TN + FN}} = \frac{\text{TN}}{\text{Predicted Negatives}} = \text{Prob( Real Negative | Predicted Negative )} \end{aligned}\)
\(\begin{aligned} \text{Lift} = \frac{\text{PPV}}{\text{Prevalence}} = \frac{\cfrac{\text{TP}}{\text{TP + FP}}}{\cfrac{\text{TP + FN}}{\text{TP + FP + TN + FN}}} \end{aligned}\)
\(\begin{aligned} \text{Net Benefit} = \frac{\text{TP}}{\text{TP + FP + TN + FN}} - \frac{\text{FP}}{\text{TP + FP + TN + FN}} * {\frac{{p_{t}}}{{1 - p_{t}}}} \end{aligned}\)
## # A tibble: 30 x 4
## model quintile phaty phatx
## <fct> <int> <dbl> <dbl>
## 1 First 1 0 0.0000975
## 2 First 2 0 0.000979
## 3 First 3 0 0.00499
## 4 First 4 0 0.0148
## 5 First 5 0.0667 0.0629
## 6 First 6 0.133 0.178
## 7 First 7 0.533 0.405
## 8 First 8 0.867 0.791
## 9 First 9 0.733 0.899
## 10 First 10 1 0.976
## # ... with 20 more rows
## [1] -0.05 1.05## # A tibble: 30 x 4
## model quintile phaty phatx
## <fct> <int> <dbl> <dbl>
## 1 First 1 0 0.0000975
## 2 First 2 0 0.000979
## 3 First 3 0 0.00499
## 4 First 4 0 0.0148
## 5 First 5 0.0667 0.0629
## 6 First 6 0.133 0.178
## 7 First 7 0.533 0.405
## 8 First 8 0.867 0.791
## 9 First 9 0.733 0.899
## 10 First 10 1 0.976
## # ... with 20 more rows
## [1] -0.05 1.05